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# Making Set-Valued Predictions in Evidential Classification: A Comparison of Different Approaches

*Proceedings of the Eleventh International Symposium on Imprecise Probabilities: Theories and Applications*, PMLR 103:276-285, 2019.

#### Abstract

In classification, it is often preferable to assign a pattern to a set of classes when the uncertainty is too high to make a precise decision. In this paper, we consider the problem of making set-valued predictions in classification tasks, when uncertainty is described by belief functions. Two approaches are contrasted. In the first one, an act is defined as the assignment to only one class, and we define a partial preorder among acts. The set of non-dominated acts is then given as the prediction. In the second approach, an act is defined as the assignment to a set of classes, and we construct a complete preorder among acts. The two approaches are discussed and compared experimentally. A critical issue both to make decisions and to evaluate decision rules is to define the utility of set-valued prediction. To this end, we propose to model the decision maker’s attitude towards imprecision using an Ordered Weighted Average (OWA) operator, which allows us to extend the utility matrix. An experimental comparison of different decision rules is performed using UCI and artificial Gaussian data sets.